Question

lim as x->-infin. of (X^5)(e^x) Use L'hospital's Rule.

Answer 1

First of all, which indeterminate form do we get here? 0/0, infinity / infinity, 0^0, infinity * infinity, etc.?

Answer 2

infinity * infinity

Answer 3

Not quite. You have -inf*(1/inf)

Answer 4

oh ok... then what? that's not one of the forms to do L'hospital's rule. so do I have to do implicit differentiation?

Answer 5

It is technically infinity*0 I believe is indeterminate.
Rewrite it as a quotient:
\[\lim_{x \rightarrow -\infty}\frac{x^5}{e^{-x}}\]
Differentiate top and bottom until you get rid of the x and you get:
\[\lim_{x \rightarrow -\infty}\frac{\frac{d^5}{dx^5}x^5}{\frac{d^5}{dx^5}e^{-x}}=\lim_{x \rightarrow -\infty}\frac{120}{-e^{-x}}=0\]

Answer 6

If I see it right.

Answer 7

\[\frac{x^5}{\frac{1}{e^x}}=\frac{x^5}{e^{-x}}\]
so e^{-x}->inf as x->-inf
x^5->-inf as x->-inf
so we have
\[\lim_{x \rightarrow -\infty}\frac{5x^4}{-e^{-x}}=\lim_{x \rightarrow -\infty}\frac{5x^4}{-e^{-x}}=\lim_{x \rightarrow -\infty}\frac{20x^3}{e^{-x}}=\lim_{x \rightarrow -\infty}\frac{60x^2}{-e^{-x}}\]
=\[\lim_{x \rightarrow -\infty}\frac{120x}{-e^{-x}}=\lim_{x \rightarrow -\infty}\frac{120}{e^{-x}}=\lim_{x \rightarrow -\infty}120e^{-x}=120\lim_{x \rightarrow -\infty}e^{-x}=\infty\]
let me check with graph

Answer 8

myininaya you brought the e^-x up as a -x!!!! Its supposed to be positive :PPPP

Answer 9

oh i see my last two steps oops

Answer 10

\[\lim_{x \rightarrow -\infty}120e^x=120 \lim_{x \rightarrow -\infty}e^x=120(0)=0\]

Answer 11

gj malevolence

Answer 12

You too :P I skipped my differentiation xP

Answer 13

i cant believe i did that

Answer 14

i dont make mistakes
in the words of satellite it was a type-0

Answer 15

:)

Answer 16

ok thank you.... why did you keep differentiating?

Answer 17

because we had indeterminate form repeatedly

Answer 18

You have to differentiate it until you get to a point where it is no longer indeterminate.

Answer 19

we kept having either \[-\frac{\infty}{\infty} or \frac{\infty}{\infty}\]
until we got to 120e^x

Answer 20

ok I see it now... thank you :)